In the United States of America, if the sitting President refuses to leave office after losing an election or getting impeached and convicted, who is responsible for physically removing them from the White House?
This case has never occurred (or even been imagined, prior to Trump), so I can only speculate. But it seems to me that it would be the job of the Secret Service. The Secret Service is tasked with protecting the President and other important political figures. As soon as a President is removed from office and a new president is sworn in, the mission of the Service shifts to protecting the new President. An old President who refuses to give up the office would constitute a threat to the new President, and that falls squarely under the Secret Service's purview.
If the Service refused to do so, then all bets are off. That shifts the context: we no longer have a recalcitrant sore loser who presents a threat to the incoming President, we have an act of organized insurrection and an attempted coup d'état. That could play out in a number of different ways involving different federal agencies.
The real answer is we don't know because it's never really happened (emphasis mine):
Experts interviewed on the possibility for this article said there is no real playbook for the scenario. Like, perhaps, the Trump administration itself, the United States would be in uncharted territory.
An article by the Atlantic notes that Presidential terms are defined be the U.S. Constitution:
The American Constitution spells out how the transfer of power is supposed to work. Article II provides that the president “shall hold his office for the term of four years.” The Twentieth Amendment says that the president’s and vice president’s terms “shall end at noon on the 20th day of January … and the terms of their successors shall then begin.” Of course, a president may be reelected to a second four-year term, but under the Twenty-Second Amendment, “no person shall be elected to the office of president more than twice.”
Given that the president would be violating constitutional law at this point, I'd imagine U.S. Courts would be able to do something about it. But that is just speculation on my part.